Find the Strain energy stored due to bending in cantilever beam subjected to UDL of intensity wkNlm over entire span.

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written 6.8 years ago by

teamques10 ★ 68k

• modified 2.8 years ago

Subject : Structural Analysis 1

Topic : General Principles

Difficulty : Low

structural analysis

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written 6.8 years ago by

teamques10 ★ 68k

Strain Energy:

$U=\int_{}^{} \frac{M^{2}}{2EI}dx$

$\Rightarrow U=\frac{1}{2EI}\int_{0}^{L} \left(\frac{wx^{2}}{2}\right)^{2}dx$

$=\frac{1}{2EI}\int_{0}^{L} \frac{w^{2}x^{4}}{4}dx$ enter image description here

$=\frac{1}{2EI}\left[\frac{w^{2}x^{5}}{20}\right]_0^L=\frac{1}{2EI}\times\frac{w^{2}L^{5}}{20}$

$U=\frac{w^{2}L^{2}}{40EI}$

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